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384783

On the dynamics of the nonlinear rational difference equation xnþ1 ¼ Axn þ Bxnk þ Cxnl þ bxnk dxnkexnl

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Last updated: 31 Dec 2024

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Abstract

In this article, we study the periodicity, the boundedness and the global stability of the
positive solutions of the following nonlinear difference equation
xnþ1 ¼ Axn þ Bxnk þ Cxnl þ
bxnk
dxnk  exnl
; n ¼ 0; 1; 2; ...
where the coefficients A;B; C; b; d; e 2 ð0;1Þ, while k and l are positive integers. The initial
conditions xl; ... ; xk; ... ; x1; x0 are arbitrary positive real numbers such that k < l. Some
numerical examples will be given to illustrate our results.

DOI

10.1016/j.joems.2014.11.002

Keywords

KEYWORDS Difference equations, Prime period two solution, Boundedness character, Locally asymptotically stable, Global attractor, Global stability

Authors

First Name

M.A.

Last Name

El-Moneam

MiddleName

-

Affiliation

Mathematics Department, Faculty of Science and Arts in Farasan, Jazan University, Saudi Arabia

Email

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Orcid

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First Name

E.M.E.

Last Name

Zayed

MiddleName

-

Affiliation

Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt

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Orcid

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Volume

23

Article Issue

3

Related Issue

50853

Issue Date

2015-10-01

Receive Date

2024-10-08

Publish Date

2015-10-01

Page Start

494

Page End

499

Print ISSN

1110-256X

Online ISSN

2090-9128

Article File

JOEMS_Volume 23_Issue 3_Pages 494-499.pdf

PDF . 680.4kB

Link

https://joems.journals.ekb.eg/article_384783.html

Detail API

https://joems.journals.ekb.eg/service?article_code=384783

Order

384,783

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Original Article

Type Code

3,248

Publication Type

Journal

Publication Title

Journal of the Egyptian Mathematical Society

Publication Link

https://joems.journals.ekb.eg/

MainTitle

On the dynamics of the nonlinear rational difference equation xnþ1 ¼ Axn þ Bxnk þ Cxnl þ bxnk dxnkexnl

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Article

Created At

21 Dec 2024